On the linear complexity and linear complexity profile of sequences in finite fields

Pseudo random sequences, that are used for stream ciphers, are required to havetheproperties of unpredictability and randomness. An important tool for measuringthese features is the linear complexity profile of the sequence in use.In this thesis we present a survey of some recent results obtained on linearcomplexity and linear complexity profile of pseudo random sequences. The relationbetween the polynomial degree and the linear complexity of a function over a finite field is given, bounds for linear complexity of the "power generator" and "the selfshrinking generator" are presented and a new method of construction of sequences of high linear complexity profile is illustrated

Multisequences with high joint nonlinear complexity

We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on the behavior of the joint nonlinear complexity of random multisequences over a fixed finite field

On joint detection and decoding of linear block codes on Gaussian vector channels

Optimal receivers recovering signals transmitted across noisy communication channels employ a maximum-likelihood (ML) criterion to minimize the probability of error. The problem of finding the most likely transmitted symbol is often equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In systems that employ error-correcting coding for data protection, the symbol space forms a sparse lattice, where the sparsity structure is determined by the code. In such systems, ML data recovery may be geometrically interpreted as a search for the closest point in the sparse lattice. In this paper, motivated by the idea of the "sphere decoding" algorithm of Fincke and Pohst, we propose an algorithm that finds the closest point in the sparse lattice to the given vector. This given vector is not arbitrary, but rather is an unknown sparse lattice point that has been perturbed by an additive noise vector whose statistical properties are known. The complexity of the proposed algorithm is thus a random variable. We study its expected value, averaged over the noise and over the lattice. For binary linear block codes, we find the expected complexity in closed form. Simulation results indicate significant performance gains over systems employing separate detection and decoding, yet are obtained at a complexity that is practically feasible over a wide range of system parameters

Investigation of multi-phase tubular permanent magnet linear generator for wave energy converters

In this article, an investigation into different magnetization topologies for a long stator tubular permanent magnet linear generator is performed through a comparison based on the cogging force disturbance, the power output, and the cost of the raw materials of the machines. The results obtained from finite element analysis simulation are compared with an existing linear generator described in [1]. To ensure accurate results, the generator developed in [1] is built with 3D CAD and simulated using the finite-element method, and the obtained results are verified with the source.The PRIMaRE project

Combinatorial Heegaard Floer homology and sign assignments

We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.Comment: 51 pages, 32 figure